Locally Private Mean Estimation: Z-test and Tight Confidence Intervals

10/18/2018

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by   Marco Gaboardi, et al.

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This work provides tight upper- and lower-bounds for the problem of mean estimation under ϵ-differential privacy in the local model, when the input is composed of n i.i.d. drawn samples from a normal distribution with variance σ. Our algorithms result in a (1-β)-confidence interval for the underlying distribution's mean μ of length Õ( σ√((1/β))/ϵ√(n)). In addition, our algorithms leverage binary search using local differential privacy for quantile estimation, a result which may be of separate interest. Moreover, we prove a matching lower-bound (up to poly-log factors), showing that any one-shot (each individual is presented with a single query) local differentially private algorithm must return an interval of length Ω( σ√((1/β))/ϵ√(n)).